In this work we investigate the transient solidification of a Lennard-Jones liquid using non-equilibrium molecular dynamics simulations and continuum heat transfer theory. The simulations are performed in slab-shaped boxes, where a cold thermostat placed at the centre of the box drives the solidification of the liquid. Two well-defined solid fronts propagate outwards from the centre towards the ends of the box until solidification is completed. A continuum phase change model that accounts for the difference between the solid and the liquid densities is formulated to describe the evolution of the temperature and the position of the solidification front. Simulation results for a small and a large nanoscale system, of sizes $30.27$,nm and $60.54$,nm, are compared with the predictions of the theoretical model. Following a transient period of $sim$20-40 ps and a displacement of the solidification front of 1-2.5 nm we find that the simulations and the continuum theory show good agreement. We use this fact to combine the simulation and theoretical approaches to design a simple procedure to calculate the latent heat of the material. We also perform simulations of the homogeneous freezing process, i.e. in the absence of a temperature gradient and at constant temperature, by quenching the liquid at supercooled temperatures. We demonstrate that the solidification rate of homogenous freezing is much faster than the one obtained under a thermal gradient for systems of the same size subject to the same thermostat temperature. Our study and conclusions should be of general interest to a wide range of atomistic solids.
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